Re: ITD algorithm equation for sound source localization

On May 2, 1:46 pm, Rune Allnor <all...@xxxxxxxxxxxx> wrote:
On 1 May, 14:51, "Sylvia" <sylvia.za...@xxxxxxxxx> wrote:

Hi
In the ITD algorithm for sound source localization,there is an equation
that needs to be solved for angle of arrival

a = d sin(theta) + d*theta

where d is radius of head and a is additional distance that sound has to
cover to reach distant ear(compared to the near ear).

My question is,if know 'a' and 'd',how we can implement the above equation
to have unique value of theta(angle of arrival).

Eh... how did you derive your equation? As far as I can tell, the
d*sin(theta) term is the difference in slant range between the two
ears and a source in the far field. What is the d*theta term? A wave
My question is,if know 'a' and 'd',how we can implement the above equation
to have unique value of theta(angle of arrival).Any MATLAB tool for
implementing the equation as LSE etc?


Hi,

You are not going to have a unique angle of arrival because this is a
line array, the angle of arrival will have an exact alias source at -
theta. In other words you to impose a physical limitation of the
source being located anywhere from 0 - 180 degress in order to have a
unique solution with line arrays.


If this is so, one way you can solve for this is using the expansion
of sine up to the degree of accuracy that you would like:

sin z= z- z^3/3! + z^5/5! - z^7/7! ...

using this and truncating it for a limited accuracy, you have

a/d = sin(theta) + theta = theta - theta^3/3! + theta^5/5! +theta =
2*theta - theta^3/3! + theta^5/5!

This polynomial can be written in a homogenous the form:

theta^5/5! - theta^3/3! + 2*theta - a/d =0

or

x^5/5! - x^3/3! + 2*x - a/d =0

So that the roots of this polynomial, which you can solve, corresponds
to your solution (see the matlab function ROOTS).
You should only consider roots that fall within the 0-pi/2 or a
multiple of it for valid solution given the requirement for uniqueness
of the angle of arrival...


There might be easier ways than that (ie, see MUSIC and beamforming),
but this is one way I can think that uses your equation....




.

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